$\bar{b}c$ susceptibilities from fully relativistic lattice QCD

TL;DR

This paper calculates various susceptibilities related to heavy quarks using relativistic lattice QCD, providing nonperturbative results for charm to bottom quark mass ratios and comparing them with perturbative predictions.

Contribution

It presents the first nonperturbative determination of tensor susceptibilities in heavy-quark systems using fully relativistic lattice QCD with multiple ensembles.

Findings

Consistent results with small nonperturbative effects at $u=m_c/m_b$

First nonperturbative tensor susceptibility results

Agreement and tension with perturbation theory at $2\sigma$ level

Abstract

We compute the $\bar{h}c$ (pseudo)scalar, (axial-)vector and (axial-)tensor susceptibilities as a function of $u=m_c/m_h$ between $u=m_c/m_b$ and $u=0.8$ using fully relativistic lattice QCD, employing nonperturbative current renormalisation and using the second generation 2+1+1 MILC HISQ gluon field configurations. We include ensembles with $a\approx 0.09\mathrm{fm}$, $0.06\mathrm{fm}$, $0.045\mathrm{fm}$ and $0.033\mathrm{fm}$ and we are able to reach the physical $b$-quark on the two finest ensembles. At the physical $m_h=m_b$ point we find $\overline{m}_b^2 \chi_{1^+}={0.720(34)\times 10^{-2}}$, $\overline{m}_b^2 \chi_{1^-}={1.161(54)\times 10^{-2}}$, $\chi_{0^-}={2.374(33)\times 10^{-2}}$, $\chi_{0^+}={0.609(14)\times 10^{-2}}$. Our results for the (pseudo)scalar, vector and axial-vector are compatible with the expected small size of nonperturbative effects at $u=m_c/m_b$. We also give the first nonperturbative determination of the tensor susceptibilities, finding $\overline{m}_b^2 \chi_{T}={0.891(44)\times 10^{-2}}$ and $\overline{m}_b^2 \chi_{AT}={0.441(33)\times 10^{-2}}$. Our value of $\overline{m}_b^2\chi_{AT}$ is in good agreement with the $\mathcal{O}(\alpha_s)$ perturbation theory, while our result for $\overline{m}_b^2\chi_{T}$ is in tension with the $\mathcal{O}(\alpha_s)$ perturbation theory at the level of $2\sigma$. These results will allow for dispersively bounded parameterisations to be employed using lattice inputs for the full set of $h\to c$ semileptonic form factors in future calculations, for heavy-quark masses in the range $1.25\times m_c \leq m_h \leq m_b$.